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J, 82 bytes g=.](]*{:@[~:])]_1}~[:>./]{~((,-)1 5 6 7)+]i.{: [:+/[:(g^:_)16,~[:,0,~0,0,0,.~0,.] Try it online! I plan to golf this more tomorrow, and perhaps write a more J-ish solution similar to thi …

J, 60 55 bytes 1}."1,/"2@((' ',.' ',":@,.){~(<|.)@(>/~)*1+#|>:*/>:)@i. Try it online! -5 thanks to xash I thought this would be a good challenge for J, and the essence of the problem is, but the form …

J, 24 20 bytes [:>./-@,|."0 2,*,=/] Try it online! -4 thanks to xash! Solved independently, but seems very similar to ovs's APL solution. This one works for any number, because I didn't notice that …

J, 66 53 bytes #{.#|.-@$(#"1~0{](]#~[-:"2*"2)#\>/#\|@-/#\)@|.]{.~3*$ Try it online! Basic Strategy We want to avoid special casing the "pad the partial top rows on the left", and "pad the partial bot …

J, 40 bytes ((2|+/~)@]+2**@[*=/~@]*(>:]*=/~))|@i:@<: Try it online!

For example, if the input is a 3 x 4 matrix, the output will be length 5 and should be interpreted as follows: the first vertical cut is minimal v 0 0 | 1 0 0 ^^^ neither horizontal cut is …

The two parts that required the most experimentation to golf were: (;/-#:i.4)&{ The phrase to pull the 4 corners from a matrix. …

J, 53 bytes <(0{]#~a:=-.&,&.>)[:(/:#@,@>)@,<<;._3&>~],@{@;&(#\)|: Try it online!

J, 37 bytes <./~@g`(|:@|.^:(1<@+>./@g=.#\.<.#\))} Try it online! Independently solved, but this approach is very similar to Lynn's. It is also one of the most perfect problems for J's little used "co …

.@+:) NB. make the inner part of the matrix 1+i.@+: NB. 1..2*n, where n is the input (] [\ 1+i.@+:) NB. fork: infixes (sliding window …

Main verb ]/:~"1/: The right most /: sorts the left arg (matrix) according to the order that would sort the right arg (specified order). This sorts rows. …

Multiplies by one minus the input, to get rid of endpoints (ie, original crosses) Add double the original matrix to that. …

J, 43 41 40 39 bytes f=.(#~1=1#.]*/ .>:|:)@~. f&.:-&.|:@f^:_ Try it online! tldr how Create a function f to filter out dominated rows. Apply plain f, followed by f "under" a negative transpose, until …

Bash, 45 44 bytes for((i=0;i<$1*$1;)){ echo $[(i/$1+i++)%$1] } Try it online! -1 thanks to dingledooper Prints flattened square, one element per line.

J, 31 bytes [:+/!@i.@99%~]+/ .*^:(<99)[:=#\ Try it online! Just implements the formula up to 99 terms, which seems to be good enough to be within 1% of the test cases.